Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
624 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C5 | C22×D32 |
| commutator, cosocle | C2×C32 | C24×C5 |
| Frattini | C2 | C22×C5×D32 |
| Fitting | C32×C5×Q8 | C22 |
| socle | C2×C32×C5 | C24 |
| hypercenter | C5×Q8 | D32 |
| hypocenter | C32 | C5×2−1+4 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2×C5 ◁ C5×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#3832 | C2 | semidirect |
| 2. C3×C5×D3×Q8 | C2 | semidirect |
| 3. C5×#3799 | C2 | semidirect |
| 4. C5×#3798 | C2 | semidirect |
| 5. C5×#3797 | C2 | semidirect |
| 16. #64316 | C5 | direct (N × H) |
| 22. C5×D3×Q8 | D3 | semidirect |
| 31. #3832 | C2×C5 | semidirect |
| 32. C3×D3×Q8 | C2×C5 | semidirect |
| 33. #3799 | C2×C5 | semidirect |
| 34. #3798 | C2×C5 | semidirect |
| 35. #3797 | C2×C5 | semidirect |
| 84. D3×Q8 | C5×D3 | semidirect |
| 87. C32×C5 | 2−1+4 | semidirect |
| 138. C3×C5 | #1007 | semidirect |
| 152. C32 | C5×2−1+4 | semidirect |
| 168. C5 | #64316 | direct (N × H) |
| 175. C3 | C5×#1007 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3832 | 2 |
| C3×C5×D3×Q8 | 2 |
| C5×#3799 | 2 |
| C5×#3798 | 2 |
| C5×#3797 | 2 |
| C5×#1007 | 3 |
| #64316 | 5 |